Partially coherent propagation-invariant beams: Passage through paraxial optical systems

The cross-spectral-density function characterizing a general propagation-invariant wave field satisfies the associated (planar) paraxial equation. Building on this result, we solve exactly the problem of the passage of such fields through arbitrary lossless optical systems characterized by their ABCD matrices. It is shown that the wave field remains shape invariant in all such systems, but that the property of strict propagation invariance is conserved only if the system is afocal. © 1991 The American Physical Society.